Why is the weight of the hinge itself not considered, or is $H_y$ the sum of the friction force upwards and the weight of the hinge downwards?
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The free body diagram on the right refers to the forces on the rod. $H_y$ is the force the hinge exerts on the rod. The weight of the hinge would be the force gravity exerts on the hinge. The hinge is attached to the wall. It is not part of the rod, so its weight is not part of the free body diagram for the rod.
answered Dec 17, 2021 at 13:02
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$\begingroup$ can you tell me what is the source of Hy $\endgroup$– noosahCommented Dec 17, 2021 at 14:19
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$\begingroup$ It's the force that the wall (via the hinge) exerts on the rod. Imagine if it were not there: the rod would simply side down the wall until the rope becomes vertical. $H_y$ is is what is stopping it slide. $\endgroup$ Commented Dec 17, 2021 at 14:26